Heat Source Function Research Articles

Convection in a porous medium with variable internal heat source and variable gravity

The qualitative effect of variable internal heat source and variable gravity on the onset of convection in a horizontal fluid saturated sparsely packed porous layer is investigated using linear stability analysis. The single term Galerkin technique is used to compute the value of the critical Rayleigh number and the corresponding wave number. Three different sets of variable gravity and heat source functions are chosen and their influence on the onset of convection is discussed. The eigenvalues are obtained for free-free velocity boundary conditions with isothermal temperature conditions on the boundaries. The influence of porous parameter on the onset of convection is brought out. It is found that the variable heat source and variable gravity does not affect the shape and size of the convective cell at the onset of convection. However the porous parameter do so.

Modeling of thermal processes proceeding in 1D domain of crystalline solids using the lattice Boltzmann method with interval source function

The interval lattice Boltzmann method (ILBM) with an uncertainly defined internal heat source function is used to simulate heat transfer in a thin silicone film. The solution to the interval Boltzmann transport equations has been obtained taking into account the rules of directed interval arithmetics. A similar analysis has been done using the sensitivity model where the Boltzmann transport equations and boundary-initial conditions have been differentiated with respect to the no-interval heat source value. The knowledge of the sensitivity function distribution and the application of the Taylor formula allow one to find the border solutions of the problem analyzed, which (to some extent) correspond to the solution obtained under the assumption of the uncertainly defined source function. In the final part of the paper, numerical computations obtained for both methods are presented.

Simplified model for polyurethane foaming in porous media

PurposeThe purpose of the study is to present a simplified model to replace the complicated foaming simulations for investigating the liquid polyurethane behavior just before solidification.Design/methodology/approachThis model is inspired from the traveling heater method of crystallization because of the low injection velocity. Besides, the heat generated during the reaction is considered as a heat source function in the energy equation.FindingsVarious distributions of the heat generation function inside the geometry have been studied to choose the most realistic one. Effect of parameters such as the soil material and porosity on the temperature distribution and flow field are examined for different values of heat flux on the boundaries. Results show an almost linear dependency of pressure drop to the velocity, a uniform velocity profile and an expected temperature distribution compared to literature, which approves the suggested model.Originality/valueA new model is presented in this study for foaming which replaces a heat generation function (exponential) in the source term of the energy equation instead of the heat produced at the exit boundary (the solid–liquid interface), and the traveling method is used instead of moving the geometry; besides, the growth ratio has been neglected; therefore, this model has been validated by a foaming simulation to confirm the suggested simplified idea.

A REVIEW OF WASTE HEAT RECOVERY BY USING THE HEAT PIPE AND THERMO-ELECTRIC GENERATOR

This paper continued a detail review of heat pipe and thermoelectric generator application in industrial, automobile and solar waste heat recovery. Each day new greenhouse gasemission further accelerates global warming. The exhaust heat recovery system by usingheat pipe and TEGsis topotentially reduce the greenhouse gases emission. The use of two specific technologies heat pipe and TEGs make passivesolid state system design. Heat pipe used in system consents more flexible design as TEG location not inadequate to exhaust pipe surface. The conversion efficiency of thermoelectric generator is function of temperature difference Heat source and heat sink temperature. The thermal performance of thermoelectric generator will be improved or enhanced by using heat pipe as a heat source in thermoelectric generator. Heat pipes do have limitations such as maximum rates of heat transfer and temperature limits. TEGs do have limitations such as low temperature limits and relatively low efficiency. When used in conjunction, these technologies have the potential to create a completely solid state and passive waste heat recovery system.

Control of thermal stresses in axissymmetric problems of fractional thermoelasticity for an infinite cylindrical domain

In this paper, we study a control problem of thermal stresses in an infinite cylindrical body. The temperature distribution is defined by the time-fractional heat conduction equation with the Caputo derivative of the order 0 < ? ? 2. The problem is formulated for axisymmetric case. The sought-for heat source function is treated as a control of stress and displacement components. For this purpose, we find the control function which guarantees the distribution of the stress component in some section of a body and at some time at a prescribed level. Integral transform technique is applied to obtain the desired control function, stresses and displacement components. Numerical results are illustrated graphically.

Influence of High Temperature Heat Sources on the Moisture and Temperature Distribution in a Real/Virtual Foundry Sand Mould

The problem described in the paper concerns the thermo-physical properties of the green mould material to which the cast iron is most often poured. The study includes the experiment of pouring the cast iron plate into green bentonite-sand mould. The temperature fields of casting and in different zones of the mould were recorded. The goal of the study was to determine the substitute thermo-physical properties of mould sand containing the over-moisture zone by means of simulation tests (inverse problem). An originality of the related research is an attempt to take into account the effects of the global thermal phenomena occurring in the quartz sand bonded by bentonite-water binder, by application of the substitute thermal coefficients without using the coupled modeling. In the simulation tests in order to achieve the effect of rapid heating of the mould (below temperatures 100 °C) by poured cast iron (T>1300 °C), the function of the latent heat source and the modified values of substitute thermal conductivity and substitute specific heat of the molding sand were used. In order to facilitate the solution, the mould was divided into zones, in which different starting humidity of molding sand was assumed.

An integral equation method to recover non-additive and non-separable heat source without initial temperature

When the unknown heat source is a non-additive and non-separable function of space–time it is very difficult to recover it. The paper proposes a more difficult mixed type inverse heat conduction problem by simultaneously recovering heat source term and unknown initial temperature, under extra measured data of boundary heat fluxes and a final time condition. We derive a domain/boundary integral equation method (DBIEM), and two different types adjoint Trefftz test functions are used to develop two different numerical algorithms, namely the DBIEM1 and the DBIEM2, which are effective and robust to recover the unknown heat source and initial value. In the adjoint Trefftz test functions we introduce a scaling factor and the multiple-scales are introduced in the trial functions, which play key roles to stabilize the resulting linear system. When we add a large absolute and relative noise up to 10% on the supplementary data, the present numerical methods are quite stable against large noise, and with a fast convergent solution of the linear system to determine the expansion coefficients, typically from five to twenty steps. It is remarkable that we can recover the general heat source function and unknown initial temperature without needing of internal measurement of temperature.

Boundary element analysis of 2D and 3D thermoelastic problems containing curved line heat sources

AbstractTemperature and stress analysis of a medium with concentrated heat sources has some important applications in engineering. In this paper, a boundary element method for analysis of two- and three-dimensional thermoelastic problems containing curved line heat sources in isotropic media is presented. In these problems, the heat generation within the problem domain is concentrated over a curved path. In the conventional integral equations of thermoelasticity, the domain integrals are expressed in terms of the temperature function. In this work, modified integral equations, in which the domain integrals are expressed in terms of the heat source function is used. The shape of the curved line heat source and the intensity function along the source can be arbitrary. Temperature, displacement and stress analyses are performed without considering internal points and without any need to find the temperature distribution in the domain. Three numerical examples are presented to show the effectiveness and accur...

The modified polynomial expansion method for identifying the time dependent heat source in two-dimensional heat conduction problems

In this paper, the modified polynomial expansion method is developed to solve problems of identifying the time dependent heat source, in which an inverse problem is encountered. Aimed at this problem, the variation of variables is adopted to eliminate the unknown heat source and obtain a six-line boundary value problem. As compared with the conventional four-line boundary value problem, the six-line boundary value problem is quite hard to be dealt with. After the unknown non-homogeneous term being eliminated, the polynomial expansion method is introduced to discretize the time and space fields, respectively. Then, the distribution of temperature is expressed as a linear superposition of polynomial functions. After that, a characteristic length concept is adopted to resolve the ill-posed matrix problems arising in those conventional polynomial expansion methods. The desired heat source function can be obtained by putting the solution of the six-line boundary value problem into differential operations. Several numerical experiments with designed examples are included to validate the accuracy and effectiveness of the proposed approach.

The interplay between the measured dimension and temperature of hot large forgings

During the forming process of hot forgings, the dimension and temperature are key parameters for improving the forging technology. In the paper, based on the mathematical physics methods, a mutual relationship model between the measured dimension and the temperature is proposed. This relationship model is displayed by the temperature field model and the dimensional model. Firstly, according to the law of conversation of energy, using the Dirichlet function and the measured dimension, the power-transfer function of heat source is established. Taking the measured temperatures as the boundary conditions, the temperature field model influenced by the dimensional change is established using the method of the moving virtual heat source. Secondly, based on the variation characteristics between the mesoscopic structure and the stress, using the function of the deformation energy is analyzed. Using the differential calculus of the pluralistic function, the dimensional change model influenced by the measured temperature is established. Based on the temperature field model and the dimensional model, this mutual relationship of the two ones can be clearly and directly displayed. Finally, the verifiable experiments and simulations are obtained using the forging experiments and the Deform-3D. Using the contrastive analysis method, the feasibility of the two relationship models is verified and the change trends of the dimension and temperature are analyzed. Combining the parameters of the forging technology in the thermal forming process, the application and the practical significance of the model are further cleared. The mutual relationship model provides a theoretical basis for improving the forging technology.

Comparison of weld characteristics between longitudinal seam and circumferential butt weld joints of cylindrical components

The control of weld induced residual stresses and distortions are very important in longitudinal seam (L-Seam) and circumferential (C-Seam) butt joints of cylindrical components. In this study, a three-dimensional, sequentially coupled thermo-metallurgical-mechanical analysis was performed for L-Seam and C-Seam butt weld joints of AISI 304 cylindrical components to evaluate weld characteristics during gas tungsten arc welding (GTAW) process. Initially, weld experiments were carried out to obtain the heat input and the macrographs which were further validated with the predicted weld molten pool sizes during heat source fitting (HSF) analysis. The Goldak's double ellipsoid heat source function obtained in HSF analysis was employed in the thermal and mechanical analysis. The results reveal that there are significant differences in residual stress distributions between L-Seam and C-Seam butt joints. Full scale shop floor welding experiments were performed to verify the effectiveness of the proposed numerical models and these are in good agreement with the experimental measurements.

Determination of Space and Time Dependent Function of Internal Heat Source in Heat Conductivity Equation

In the present work we propose the method for the solution inverse heat conduction problem that consists of the identification of unknown internal heat source function depending simultaneously on space and time variables. The source function can be represented as a separable variable. We consider an inverse problem of determining the heat source function based on temperature measurements.Inverse problem is formulated as an optimization problem, a variational formulation for solving the optimization problem is given. The estimation of internal heat source is investigated with the analytical method combined with the method for approximate modal definition of temperature state and source function. The temperature state and desired control input are represented in the form of finite expansion in terms of orthogonal system of eigenfunctions. The required eigencoefficients of temperature state can be determined using temperature measurements. Then eigencoefficients of heat source function can be defined sequentially.Some numerical examples are provided to show the efficiency of the proposed method.

An iterative algorithm for identifying heat source by using a DQ and a Lie-group method

We develop a novel yet simple iterative algorithm to solve a mixed-type inverse heat conduction problem, which is a combination of the Cauchy problem, the backward heat conduction problem (BHCP) and a heat source recovery problem. First, we transform the heat conduction equation into a new one, including a spring term and a damping term, which can raise the accuracy of numerical solution. Second, we use the differential quadrature method to semi-discretize the differential term, and then the group-preserving scheme leads to an accurate solution of the mixing Cauchy and BHCP. Third, with the aid of an overspecified right-end boundary condition, an iterative Lie-group adaptive method is developed to recover the space-dependent heat source function through a few iterations. The heat source term recovered is quite smooth, even the input data are polluted by a random noise, being large up to . The accuracy and efficiency of the new methods are assessed by comparing the estimated results with exact solutions from several numerical examples.

Photophoresis of spherical particles with interfacial thermal resistance in micro–nano fluids

Based on Mie scattering theory and steady thermal conduction function, we establish the theoretical analysis of particlesʼ photophoresis in micro–nano fluids by taking into account the interfacial resistance between particles and the fluid. It is found that the heat source function can determine not only the magnitude but also the direction of the photophoretic velocity, while the interfacial resistance can only play a role in the magnitude of the velocity. Numerical results show that there is positive (negative) photophoresis for particles with large (small) size parameter α , high (low)-absorption κ p , and low (high)-refraction n p . In addition, lower thermal conductivity and smaller interfacial resistance of the particle may result in faster photophoretic motion. • We establish the theory for photophoresis in micro–nano fluids. • We consider the effect of interfacial resistance on photophoresis. • The HSF can determine the magnitude and direction of photophoresis. • The interfacial resistance can only determine the magnitude of photophoresis. • Lower k p and R k may result in faster photophoretic motion.

Experimental and finite element analysis of temperature and energy partition to the workpiece while grinding with a flexible robot

Grinding processes performed with flexible robotic tool holders are very unlike conventional types of grinding because of low stiffness of the robot's structure. A special flexible robotic grinding process is used for in situ maintenance of large hydroelectric equipment for bulk material removal over large areas rather than as a finishing step, as is the case for most conventional grindings. Due to the low structural stiffness of tool holder, cutting is interrupted at each revolution of wheel during the grinding process. In this study, an investigation is carried out to determine the temperatures and energy partition to the workpiece for the above-mentioned flexible robotic grinding process by a three-dimensional finite element thermal model. Experiments were undertaken using embedded thermocouples to obtain the subsurface temperature at several points in the workpiece during the process. Then, energy partition to the workpiece was evaluated using a temperature-matching method between the experimental and numerical results. This ratio is used for predicting the temperature field at the wheel–workpiece interface with a relevant heat source function. Kinematics of cut and the flexible robot's dynamic behavior are considered in applying the heat input to the model. The energy partition to the workpiece in this specific flexible grinding process is found to be lower than for analogous conventional precision grinding processes. Two models, one from the literature and one from the power model of the process, are modified and proposed for determining the energy partition. The results showed that the energy partition ratio decreases by increasing the process power. Also, this ratio slightly decreases at higher feed speeds. In addition, lower temperatures were seen at higher powers due to the lower intensity of heat input over a larger contact area. Experimental observations show close agreement between simulated contact temperatures and measured results.

Application of scaled nonlinear conjugate-gradient algorithms to the inverse natural convection problem

The inverse natural convection problem (INCP) in a porous medium is a highly nonlinear problem because of the nonlinear convection and Forchheimer terms. The INCP can be converted into the minimization of a least-squares discrepancy between the observed and the modelled data. It has been solved using different classical optimization strategies that require a monotone descent of the objective function for recovering the unknown profile of the time-varying heat source function. In this investigation, we use this partial differential equation (PDE)-constrained optimization problem as a demanding test bed to compare the performance of several state-of-the-art variants of the conjugate gradients approach. We propose solving the INCP, using the scaled nonlinear conjugate gradient method: a low-cost and low-storage optimization technique. The method presented here uses the gradient direction with a particular spectral step length and the quasi-Newton Broyden–Fletcher–Goldfarb–Shanno updating formula without any matrix evaluations. Two adaptive line search approaches are numerically studied in which there is no need for solving the sensitivity problem to obtain the step length directly, and are compared with an exact line search approach. We combine the proposed optimization scheme for INCP with a consistent-splitting scheme for solving systems of momentum, continuity and energy equations and a mixed finite-element method. We show a number of computational tests that demonstrate that the proposed method performs better than the classical gradient method by improving the number of iterations required and reducing the computational time. We also discuss some practical issues related to the implementation of the different methods.

Reconstruction of a space and time dependent heat source from finite measurement data

This paper deals with an inverse problem of determining a heat source function in heat conduction equations when the solution is known in a discrete point set. Being different from other ordinary inverse source problems which are often dependent on only one variable, the unknown coefficient in this paper not only depends on the space variable x, but also depends on the time t. On the basis of the optimal control framework, the inverse problem is transformed into an optimization problem. The existence and necessary condition of the minimizer for the cost functional are established. The convergence of the minimizer as the mesh parameters tend to zero is also proved. The conjugate gradient method is applied to the inverse problem and some typical numerical experiments are performed in the paper. The numerical results show that the proposed method is stable and the unknown heat source is recovered very well.

Theoretical Analysis of Cylindrical Microparticle Photophoresis in a Perpendicular Optical Field with Thermal Stress Slip Model

ABSTRACTThe present study is concerned with a theoretical analysis of the photophoresis of a microsized long cylinder in a perpendicular optical field. Different from previous studies of photophoresis, thermal stress slip usually neglected is taken into account in the analysis. The gaseous fluid relative to the microparticle in photophoretic motion falls into slip-flow regime. Asymmetric distribution of the absorbed heat energy within the particle becomes the driving force for photophoretic motion of the cylinder-shaped particle. By evaluating heat source function distributions at various conditions, the study focuses on the effects of particle size and optical properties on the energy distribution and the resultant influences on the photophoresis. The photophoretic mobility is developed by the slip flow model with consideration of thermal stress slip. The results reveal that the photophoretic mobility decreases with the increase of particle thermal conductivity (k*) and increases with Knudsen number (Kn). The thermal stress slip effect on photophoretic velocity is more noticeable at high Kn, but disappears at the continuum limit. A long cylinder-shaped particle has higher photophoretic velocity than a spherical particle at low k*, while the situation reverses at high k*. With thermal stress slip considered, the critical condition for crossing of the photophoretic velocity curves of cylindrical and spherical particles is mildly influenced by Kn.

Thermo-responsive adhesion properties of composite hydrogel microcapsules

The present work describes the synthesis and characterisation of thermo-responsive microcapsules consisting of poly-N-isopropylacrylamide (PNIPAM) hydrogel, hydrophilic citrate-stabilized super-paramagnetic iron oxide nanoparticles (SPIONs) that perform the function of a local heat source and hydrophobic nanoparticles (either SiO2 or oleic acid-coated SPIONs) that stabilize the microcapsule surface. The microcapsules have been synthesized by the inverse Pickering emulsion polymerisation method. The effect of iron oxide concentration in the hydrogel on the shape, size, shrinkage ratio and heating rate of the microcapsules has been systematically investigated. The adhesion properties of the composite microcapsules towards a range of substrates have been characterised in a microfluidic flow cell and it was found that the temperature-induced change of the microcapsule size is an effective way of controlling adhesion. The induction heating of the embedded SPIONs makes it possible to control adhesion remotely in environments where macroscopic heating is not possible.

CAE 를 통한 하이브리드 용접 후 차체부품 변형예측 및 검증

In recent years, laser-arc hybrid welding has begun to be adopted for assembly welding of automotive bodies and parts, because the hybrid welding process can weld lapped steel sheets having a larger gap than is possible with laser welding. In this paper, to predict the twist deformation by the hybrid welding when brackets are welded in B pillar of a passenger car, the residual stress using CAE is analyzed and the deformation result of CAE is compared with the measured deformation. First of all, after modeling heat source as intended to be expressed with laser-arc hybrid welding method, heat source fitting is done with welding conditions and a section of welding part obtained through specimen test. In case of heat source functions, laser used conical source and arc used double ellipsoid source. Through the local model analysis, elements which are located in the center of the model are selected. The elements are called WME(Welding Macro Element). This WME is extruded in the welding lines and welding phenomenon of complex parts is accomplished. The deformation amount after hybrid welding is got through a simulation, the validity of simulation is verified by measuring the panel and comparing with the simulation result.